Welcome to Seunghun Lee(이승훈)'s Math page!

Hello! I am an Assistant Professor in the Department of Mathematics at Keimyung University (계명대학교), Daegu, South Korea.

I had wonderful postdoc opportunities previously at

IBS Discrete Mathematics Group (DIMAG) (CI: Prof. Oum, Sang-il 엄상일), Daejeon, South Korea (Jul. 2025 - Aug.2025) as a postdoctoral research fellow,
Department of Mathematical Sciences, KAIST, Daejeon, South Korea (Feb. 2024 - Jun. 2025) as a BK21 Research Assistant Professor,
Einstein Institute of Mathematics, Hebrew University of Jerusalem (under Prof. Eran Nevo and Prof. Gil Kalai) Jerusalem, Israel (Aug. 2022 - Jan. 2024) as a postdoctoral research fellow, and
Department of Mathematics and Statistics, Binghamton University (SUNY Binghamton, Mentor: Prof. Michael Gene Dobbins), Binghamton, New York, USA (Sep. 2020 - Jul. 2022) as a Robert Riley Visiting Assistant Professor.

Prior to it, I was fortunate enough to be a graduate student at KAIST under supervision of Prof. Andreas Holmsen. Under his generous guidance, I learned the world of discrete geometry and topological combinatorics, and I got an M.S. at 2015 and a Ph.D. at 2020 specialized in this area (see my dissertations in below!). I also had a wonderful opportunity to visit Tokyo Institute of Technology (東京工業大学, Tokyo, Japan) via the Campus Asia program from Oct. 2015 to Feb. 2016. Through guidance of Prof. Tamás Kálmán, I learned interesting aspects of geometric combinatorics.

Roughly speaking, I am interested in combinatorial properties of geometric objects. These include, but are not restricted to, combinatorial properties of simplicial complexes such as transversal numbers and coloring, combinatorial convexity and its topological extension, rainbow problems, and order types (or oriented matroids).

For more information, please check my CV.

E-mail: seunghun (dot) math (at) gmail (dot) com

ORCID: https://orcid.org/0000-0003-0838-1680

Publications

Papers/Preprints

10. S. Lee, The interval coloring impropriety of planar graphs. Discrete Applied Mathematics. 370, (2025), 88-91. (arXiv)

9. S. Lee and Shakhar Smorodinsky, On conflict-free colorings of cyclic polytopes and the girth conjecture for graphs. preprint. (2024) (arXiv)

8. S. Lee and Eran Nevo. On colorings of hypergraphs embeddable in R^d. preprint. (2023) (arXiv)

7. Michael Gene Dobbins and S. Lee. Inscribable order types. Discrete & Computational Geometry. 72, Issue 2 (Eli Goodman Memorial Isuue) (2024), 704–727. (arXiv)

6. Joseph Briggs, Michael Gene Dobbins and S. Lee. Transversals and colorings of simplicial spheres. Discrete & Computational Geometry. 71 (2024), 738–763. (arXiv)

5. Andreas Holmsen and S. Lee. Leray numbers of complexes of graphs with bounded matching number. Journal of Combinatorial Theory, Series A. 189 (2022), Article 105618. (arXiv)

4. Tamás Kálmán, S. Lee and Lilla Tóthmérész. The sandpile group of a trinity and a canonical definition for the planar Bernardi action. Combinatorica. 42 (2022), 1283-1316. (Arxiv)

3. Andreas Holmsen, Minki Kim and S. Lee. Nerves, minors, and piercing numbers. Trans. Amer. Math. Soc. 371 (2019), 8755-8779. (Arxiv)

2. S. Lee and Kangmin Yoo. On a conjecture of Karasev. Computational Geometry: Theory and Applications. 75 (2018), 1-10 (Arxiv)

1. Andreas Holmsen and S. Lee. Orthogonal colorings of the sphere. Mathematika 62 (2016), 492 - 501. (Arxiv)

Other manuscripts

Ph.D. Thesis: Topology of complexes of graphs with bounded matching number, 2020. (link)
In the paper, Linusson, Shareshian, and Welker considered the homotopy type of the non-matching complex of a graph G when G is either a complete graph or a complete bipartite graph. In this thesis, we consider an analogue scenario which focuses more on vanishing homology groups but a given graph G is not limited to complete graphs or complete bipartite graphs. That is, we prove the near Leray property of the non-matching complex of a graph G. This topological result implies a sufficient condition for the existence of a rainbow matching. This work is an extended version of the paper ``Leray numbers of complexes of graphs with bounded matching number".
Master Thesis: Combinatorial geometry on the sphere, 2015. (link)
In this thesis, we prove some new results on colorings on the sphere and oriented matroids. For colorings on the sphere, we first give a slightly different, but essentially same result as in the paper ``Orthogonal colorings of the sphere". As the consequence of the proof, we prove the conjecture given by Jonathan Noel. For oriented matroids, we first prove a generalization of Theorem 2 in the paper ``Points Surrounding the Origin" to the oriented matroid version. Next, we prove a version of Ham-Sandwich theorem for oriented matroids.

Teaching experience

@ Keimyung University (계명대학교)

Fall 2025 (current): Linear Algebra (2) (Korean: 선형대수학(2), 14290-01), Elementary Number Theory (Korean: 정수론, 16903-01), Discrete Mathematics (Korean 이산수학, 21683-01).

@ KAIST

Spring 2025 : Calculus 1 (MAS101).
Fall 2024 : Calculus II (MAS102).
Spring 2024 : Calculus 1 (MAS101).

@ Binghamton University

Spring 2022 : Graph theory (MATH381).
Fall 2021 : Differential/Integral Calculus (MATH224/225), Discrete Mathematics (MATH314).
Spring 2021: Number Systems (MATH330).
Fall 2020: Linear Algebra (MATH304), Discrete Mathematics (MATH314).

@ KAIST (as a Teaching Assistant)

Spring 2020: Probablity and Statistics (CC511).
Fall 2019: College Mathematics (MAS100).
Spring 2019: Introduction to Linear Algebra (MAS109).
Fall 2018: College Mathematics (MAS100).
Spring 2018: Calculus I (MAS101) (I received the outstanding TA award).
Winter 2017-2018 Online T.A.: College Mathematics (MAS100) (for the Bridge Program).
Fall 2017 Tutor: College Mathematics (MAS100) (for international students).
Spring 2017: Calculus I (MAS101), Discrete Geometry (MAS478).
Fall 2016: College Mathematics (MAS100), Linear Algebra (MAS212).
Spring 2016: Calculus I (MAS101), Discrete Mathematics (MAS275).
Spring 2015: Discrete Mathematics (MAS275).
Fall 2014: Calculus II (MAS102).

(last updated: September 6. 2025.)

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